Question

Characteristic Equation for Traceless Matrices

score 157 · Answer 1 · 2021-07-15 18:15:59

157

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Characteristic Equation for Traceless Matrices

Published on 15 Jul 2021 - 18:15

score 130 · Answer 2 · 2021-07-18 01:16:17

130

Views

Convert recursive formula w exponent to explicit

Published on 18 Jul 2021 - 1:16

score 85 · Answer 3 · 2021-07-23 05:03:34

85

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Are the matrices diagonalizable in the field $K$?

Published on 23 Jul 2021 - 5:03

score 370 · Answer 4 · 2021-08-03 09:09:05

370

Views

Let $P_A(x)$ denote the characteristic polynomial of a matrix $A$. Let $P_A(x)-P_{A^{-1}}(x) = c$......(1), where $c$ is a constant.

Published on 03 Aug 2021 - 9:09

score 90 · Answer 5 · 2021-08-09 03:12:13

90

Views

How to show that the minimal polynomial and the characteristic polynomial has the same set of roots?

Published on 09 Aug 2021 - 3:12

score 125 · Answer 6 · 2026-03-25 22:06:01

125

Views

Prove that $P^k=P$ for any $k \in \mathbb{N}$ where $1$ is the only eigenvalue of $P$ implies $P=I$.

Published on 25 Mar 2026 - 22:06

score 85 · Answer 7 · 2021-08-11 23:13:44

85

Views

What is the fastest way to find the characteristic polynomial of $4\times4$ matrix and its change of basis matrix?

Published on 11 Aug 2021 - 23:13

score 74 · Answer 8 · 2021-08-12 09:11:50

How to find characteristic polynomial of a matrix $A$ whose elements are of the form $a_{ij} = a_ia_j$ for all $1\leq i,j \leq n$

score 103 · Answer 9 · 2021-08-13 22:15:44

103

Views

Conjugacy of linear transformations with the same characteristic polynomial

Published on 13 Aug 2021 - 22:15

score 362 · Answer 10 · 2021-08-21 14:55:23

362

Views

Why is the algebraic multiplicity the dimension of the kernel of $(A-\lambda I)^q$, where $\ker(A-\lambda I)^q=\ker(A-\lambda I)^{q+1}$?

Published on 21 Aug 2021 - 14:55

score 92 · Answer 11 · 2021-08-26 01:46:46

92

Views

Let $A_{n×n}$ be a complex matrix then prove that $ch_{AB}(x) = ch_{BA}(x)$

Published on 26 Aug 2021 - 1:46

score 563 · Answer 12 · 2021-08-28 19:31:48

563

Views

Defining the characteristic polynomial of an endomorphism through its properties instead of a formula

Published on 28 Aug 2021 - 19:31

score 327 · Answer 13 · 2021-09-07 19:17:36

327

Views

generic matrix similar to companion matrix of its minimal polynomial

Published on 07 Sep 2021 - 19:17

score 144 · Answer 14 · 2021-09-07 22:50:10

144

Views

If $m$ is the multiplicity of $\lambda$ as a root of the char poly of $T$, prove that $W_m=W_{m+1}$, where $W_i=\{v\in V|(T-\lambda I)^i(v)=0\}$

Published on 07 Sep 2021 - 22:50

score 187 · Answer 15 · 2021-09-08 18:52:07

187

Views

Simple root of characteristic polynomial of matrix over a commutative ring

Published on 08 Sep 2021 - 18:52

List Question

Characteristic Equation for Traceless Matrices

Convert recursive formula w exponent to explicit

Are the matrices diagonalizable in the field $K$?

Let $P_A(x)$ denote the characteristic polynomial of a matrix $A$. Let $P_A(x)-P_{A^{-1}}(x) = c$......(1), where $c$ is a constant.

How to show that the minimal polynomial and the characteristic polynomial has the same set of roots?

Prove that $P^k=P$ for any $k \in \mathbb{N}$ where $1$ is the only eigenvalue of $P$ implies $P=I$.

What is the fastest way to find the characteristic polynomial of $4\times4$ matrix and its change of basis matrix?

How to find characteristic polynomial of a matrix $A$ whose elements are of the form $a_{ij} = a_ia_j$ for all $1\leq i,j \leq n$

Conjugacy of linear transformations with the same characteristic polynomial

Why is the algebraic multiplicity the dimension of the kernel of $(A-\lambda I)^q$, where $\ker(A-\lambda I)^q=\ker(A-\lambda I)^{q+1}$?

Let $A_{n×n}$ be a complex matrix then prove that $ch_{AB}(x) = ch_{BA}(x)$

Defining the characteristic polynomial of an endomorphism through its properties instead of a formula

generic matrix similar to companion matrix of its minimal polynomial

If $m$ is the multiplicity of $\lambda$ as a root of the char poly of $T$, prove that $W_m=W_{m+1}$, where $W_i=\{v\in V|(T-\lambda I)^i(v)=0\}$

Simple root of characteristic polynomial of matrix over a commutative ring

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